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Oriented Fuzzy Numbers vs. Fuzzy Numbers

Author

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  • Krzysztof Piasecki

    (Institute of Economy and Finance, WSB University in Poznan, ul. Powstańców Wielkopolskich 5, 61-895 Poznań, Poland)

  • Anna Łyczkowska-Hanćkowiak

    (Institute of Economy and Finance, WSB University in Poznan, ul. Powstańców Wielkopolskich 5, 61-895 Poznań, Poland)

Abstract

A formal model of an imprecise number can be given as, inter alia, a fuzzy number or oriented fuzzy numbers. Are they formally equivalent models? Our main goal is to seek formal differences between fuzzy numbers and oriented fuzzy numbers. For this purpose, we examine algebraic structures composed of numerical spaces equipped with addition, dot multiplication, and subtraction determined in a usual way. We show that these structures are not isomorphic. It proves that oriented fuzzy numbers and fuzzy numbers are not equivalent models of an imprecise number. This is the first original study of a problem of a dissimilarity between oriented fuzzy numbers and fuzzy numbers. Therefore, any theorems on fuzzy numbers cannot automatically be extended to the case of oriented fuzzy numbers. In the second part of the article, we study the purposefulness of a replacement of fuzzy numbers by oriented fuzzy numbers. We show that for a portfolio analysis, oriented fuzzy numbers are more useful than fuzzy numbers. Therefore, we conclude that oriented fuzzy numbers are an original and useful tool for modelling a real-world problems.

Suggested Citation

  • Krzysztof Piasecki & Anna Łyczkowska-Hanćkowiak, 2021. "Oriented Fuzzy Numbers vs. Fuzzy Numbers," Mathematics, MDPI, vol. 9(5), pages 1-27, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:523-:d:509396
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    References listed on IDEAS

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    1. Krzysztof Piasecki & Anna Łyczkowska-Hanćkowiak, 2019. "Representation of Japanese Candlesticks by Oriented Fuzzy Numbers," Econometrics, MDPI, vol. 8(1), pages 1-24, December.
    2. Anna Łyczkowska-Hanćkowiak & Krzysztof Piasecki, 2018. "The present value of a portfolio of assets with present values determined by trapezoidal ordered fuzzy numbers," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 28(2), pages 41-56.
    3. Aleksandra Wójcicka-Wójtowicz & Anna Łyczkowska-Hanćkowiak & Krzysztof Piasecki, 2020. "Application of the SAW Method in Credit Risk Assessment," Springer Proceedings in Business and Economics, in: Krzysztof Jajuga & Hermann Locarek-Junge & Lucjan T. Orlowski & Karsten Staehr (ed.), Contemporary Trends and Challenges in Finance, pages 189-205, Springer.
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    Cited by:

    1. Anna Łyczkowska-Hanćkowiak & Aleksandra Wójcicka-Wójtowicz, 2023. "On portfolio analysis using oriented fuzzy numbers for the trade-related sector of the Warsaw Stock Exchange," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 33(4), pages 155-170.

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